The present invention relates to an X-ray CT apparatus and a method of controlling it.
The current mainstream X-ray CT apparatus implements a filtered backprojection technique involving processes of data collection, preprocessing, filtering, backprojection processing, and post-processing to thereby reconstruct an image.
Conventional backprojection processing is disclosed in, for example, Japanese Patent Application Laid Open No. H8-187241 and U.S. Pat. No. 5,414,622.
In such backprojection processing, projection data D0(view, ch) obtained by a fan beam represented by a view angle view and a detector channel ch is subjected to a calculation for projecting the projection data D0(view, ch) onto coordinates (x, y) of a pixel constituting a reconstruction region to determine pixel projection data D2(x, y), and the pixel projection data D2(x, y) for all views used in image reconstruction are added to determine backprojection data D3(x, y).
The conventional method of determining backprojection data D3, however, often employs an arctan lookup table LUT to speed up a calculation of determining a distance from an X-ray focal spot to a reconstruction plane. At that time, it is assumed that the positional relationship between the X-ray focal spot and X-ray detector is in proper alignment; specifically, that the X-ray focal spot lies on a centerline (or if ¼ channel shifting is applied, a centerline shifted by a ¼ channel) of the arc-shaped X-ray detector. FIG. 20 shows the X-ray focal spot and the X-ray detector with their positional relationship in proper alignment.
In FIG. 20, reference numeral 2000 designates an X-ray focal spot; 2001 designates an X-ray detector; 2001a and 2001b designate reference channels of the X-ray detector 2001; and 2002a and 2002b designate X-rays impinging upon the reference channels 2001a and 2001b. 
The reference channels 2001a and 2001b are channels at ends among those of the X-ray detector 2001, and they detect X-rays emitted from the X-ray focal spot 2000 not passing through a subject. If the reference channels 2001a and 2001b detect the same amount of X-rays, the position of the X-ray focal spot 2000 and the position of the X-ray detector 2001 are considered to be in proper alignment. At the same time, the length of the X-ray 2002a (the straight-line distance from the X-ray focal spot 2000 to the reference channel 2001a) is equal to the length of the X-ray 2002b (the straight-line distance from the X-ray focal spot 2000 to the reference channel 2001b). However, such alignment is cumbersome and difficult to achieve precisely.